Study on Optimal Design Based on Direct Coupling Between a FEM Simulation Model and L-BFGS-B Algorithm

Berkani, Mohamed Saïd; Giurgea, Stéfan; Espanet, Christophe; Coulomb, Jean‐Louis; Kieffer, Christophe

doi:10.1109/tmag.2013.2245871

Cited by 17 publications

(5 citation statements)

References 10 publications

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“…Thus, L-BFGS has attracted considerable attention and has been used to solve many practical problems. For further information, see [35][36][37] for general methods and [38,39] for applications.…”

Section: Limited Memory Bfgs Methodsmentioning

confidence: 99%

A hybrid approach to constrained global optimization

Liu

Zhang²,

et al. 2016

Applied Soft Computing

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a b s t r a c tIn this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.

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Section: Limited Memory Bfgs Methodsmentioning

confidence: 99%

A hybrid approach to constrained global optimization

Liu

Zhang²,

et al. 2016

Applied Soft Computing

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“…The first loss term satisfies the initial and boundary conditions, the second term corresponds to the residuals of the small sample data on the domain and the third term serves as a constraint on the governing equation itself. The optimization method used here is L-BFGS-B algorithm [29], which converges faster in calculations and has lower memory overhead.…”

Section: Loss Function and Algorithmmentioning

confidence: 99%

LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential燛quations

Liu¹,

Xu²,

Mei³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of the theoretical support of traditional numerical method and the efficient allocation of modern machine learning, LaNets achieve higher predictive accuracy compared to the state-of-the-art work. The stability and accuracy of the proposed algorithm are demonstrated through a series of classical numerical examples, including one-dimensional Burgers equation, onedimensional carburizing diffusion equations, two-dimensional Helmholtz equation and two-dimensional Burgers equation. Experimental results validate the robustness, effectiveness and flexibility of the proposed algorithm.

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“…The gradient can be approximated using finite-difference. However, numerical noise due to re-meshing makes this approximation highly sensitive and requires adjusting the step size used for the computation [3]. Thus, the use of such an algorithm is not beneficial and a gradient of good quality need to be computed.…”

Section: Finite-differencementioning

confidence: 99%

“…Thus, these issues have been extensively studied in the literature using the metamodel approach and the stochastic algorithms [1,2], e.g., genetic algorithms (GA), etc. On the other hand, optimization using gradient-based algorithms is less studied due to the remeshing error that perturbs the gradient's computation using the finite difference technique [3].…”

Section: Introductionmentioning

confidence: 99%

Branch and Bound Algorithm Based on Prediction Error of Metamodel for Computational Electromagnetics

et al. 2020

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Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

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Study on Optimal Design Based on Direct Coupling Between a FEM Simulation Model and L-BFGS-B Algorithm

Cited by 17 publications

References 10 publications

A hybrid approach to constrained global optimization

A hybrid approach to constrained global optimization

LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential燛quations

Branch and Bound Algorithm Based on Prediction Error of Metamodel for Computational Electromagnetics

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